In this paper we introduce a coordination-restrained
path integral molecular dynamics (PIMD) method
based on an explicit solvent model to study the p\(K_W\)  of
liquid water and its isotopologues.
PIMD is a rigorous approach that takes account of
both nuclear quantum and temperature effects based on
the imaginary-time path integral theory
for quantum statistical mechanics
[1]}, [2]}, [3]}, [4]}, [5]}.
PIMD has been used to study the NQEs on several properties of water as
summarized in a recent review.[6]}
